The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that combines linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number of instances, even for those with many items.

翻译：有色装箱问题（CBPP）是装箱问题（BPP）的一种推广形式。该问题要求将一组具有重量和颜色的物品装入容量有限的箱子中，目标是最小化所用箱子数量，并满足同一箱子中相同颜色的物品不能相邻放置的约束条件。本文针对CBPP提出了BPP启发式算法的改进版本以及新的启发式算法。此外，我们设计了一套用于CBPP的快速邻域搜索算法。这些邻域结构被应用于基于变邻域搜索（VNS）的元启发式方法，以及一种将线性规划与元启发式方法（包括VNS和贪心随机自适应搜索（GRASP））相结合的数学启发式方法。实验结果表明，我们的数学启发式方法优于VNS，且两种方法均能在大量实例（包括包含众多物品的实例）中找到近似最优解。